There is two ways to begin with you're items as Lux. You either start by buying a Doran's Ring, because of the extra AP, HP and Mana Regen, whichs is very much needed in the start, before you're jungler start letting you have the Crest of the Ancient Golem instead of himself.
Then you can also start out with Boots and 3 Health Potion. If you know how to dodge the spells from of you're mid enemy, then you're better off taking the Doran's Ring instead. This option is mainly just to make sure that you don't give you're opponent a easy kill on you, by not moving quickly enough out of his attacks. This would mainly be aganist champions like Ahri, Katarina, Brand and ofcouse an enemy Lux in normal games. The extra movement speed can also be a huge life saver combinded with you're slowing effect from Lucent Singularity and Light Binding, against ganks by either the jungler or other lanes.